Effect of Proximity of Permeable and Impermeable Lenses on Well Performance

A study was made of the effect of permeable and impermeable lenses in a reservoir on the production capacity of a well. Both steady-state and unsteady-state data were obtained. An electrical resistivity model was used to obtain the steady- state data and thermal models were constructed to obtain the unsteady-state data. The productivity of a well is affected very greatly only when the lenses are close to the well. The effect of circular lenses on the Productivity ratio can be correlated with the distance from the center of the lens to the center of the well divided by the radius of the lens. Then this dimensionless distance is equal to six or greater, the effect of the lenses on production capacity will be negligible. The pseudo steady-state productivity of a heterogeneous reservoir can be predicted using steady- state data. Introduction Many analytical solutions of reservoir behavior assume that reservoir rock is uniform and homogeneous. Although this assumption is used, all of the data from core analyses and well logging indicate that the reservoirs are heterogeneous. Very little work has been done on the performance of heterogeneous reservoirs. The work of Landrum, et al. showed that transient phenomena in oil reservoirs could be studied with thermal models. Pickering and Cotman used thermal models to study flow in stratified reservoirs and investigated the effect of inhomogeneities in oil reservoirs on transient flow performance. Loucks made a mathematical study of the pressure build-up in a system composed of two concentric regions of different permeability. Root, Silberberg and Pirson studied the effect of me growth of the flooded region on water influx predictions using a thermal model consisting of three concentric cylindrical regions of different thermal properties which simulated the aquifer, the flooded region and the unflooded portion of the original hydrocarbon region. Tomme, et al. made a mathematical study of vertical fractures. The object of this investigation was to study the effect of highly permeable and impermeable lenses in the vicinity of the wellbore on the pressure depletion history of the well. Steady- state data were obtained for both conductive and nonconductive lenses that completely penetrated the formation. The lenses were symmetrically located at various distances from the wellbore. The unsteady-state data were obtained on seven thermal models. EXPERIMENTAL EQUIPMENT AND PROCEDURE STEADY-STATE DATA The steady-state data were obtained from an electrical resistivity model 30 in. in diameter and approximately 1 1/2 in. deep. The outside of the model was lined with a 30-in. diameter copper strip, which served as the outer boundary of the reservoir. The bottom was covered with a sheet of plexiglass so that it would be nonconductive. The model was filled with a slightly saline solution. The well size was varied from an 0.064-in. diameter copper wire to a 10-in. diameter copper cylinder. Readings were taken with an impedance bridge using AC current to prevent polarization at the contacts. Copper and wax lenses were used to represent infinitely conductive and nonconductive lenses, respectively. The resistance was first measured for each well diameter with no lenses in the reservoir. Then the conductive and nonconductive lenses were spaced symmetrically at various distances from the well and the resistance read from each lens location. The diameters of the conductive lenses were 3, 1.022 and 0.624 in., and those of the nonconductive lenses were 3, 2.25 and 1.563 in. SPEJ P. 285ˆ